What is the solution for (dy)/(dx)=(y-1)(1-2y) ?

The solution for (dy)/(dx)=(y-1)(1-2y) is y=-(e^{x+c_{1}})/(1-e^{x+c_{1)}}+1/(2(1-e^{x+c_{1)})}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(dy)/(dx)=(y-1)(1-2y)

\frac{d y}{d x} = (y - 1) (1 - 2 y)

y = - \frac{e ^{x + c_{1}}}{1 - e ^{x + c_{1}}} + \frac{1}{2 ( 1 - e ^{x + c_{1}} )}

Solution steps

\frac{d y}{d x} = (y - 1) (1 - 2 y)

Solve separable ODE:

y = - \frac{e ^{x + c_{1}}}{1 - e ^{x + c_{1}}} + \frac{1}{2 ( 1 - e ^{x + c_{1}} )}

y = - \frac{e ^{x + c_{1}}}{1 - e ^{x + c_{1}}} + \frac{1}{2 ( 1 - e ^{x + c_{1}} )}

What is the solution for (dy)/(dx)=(y-1)(1-2y) ?
The solution for (dy)/(dx)=(y-1)(1-2y) is y=-(e^{x+c_{1}})/(1-e^{x+c_{1)}}+1/(2(1-e^{x+c_{1)})}